Abstract

A fast radiative transfer model has been developed for prelaunch
simulation studies of Infrared Atmospheric Sounding Interferometer
(IASI) data and for the exploitation of IASI radiances within the
framework of a numerical weather prediction variational analysis
scheme. The model uses profile-dependent predictors to parameterize
the atmospheric optical depths and is fast enough to cope with the
processing of observations in near real time and with the several
thousands of transmittance calculations required to simulate radiances
from a full range of atmospheric conditions. The development of the
model has involved the selection of a training set of atmospheric
profiles, the production of a line-by-line transmittance database, the
selection of optimal predictors for the gases considered in the study,
and the production of regression coefficients for the fast
transmittance scheme. The model fit to the line-by-line radiances
shows that it can reproduce the line-by-line radiances to a degree of
accuracy that is at or below the instrumental noise.

Histogram of frequency by bin number and pressure level
for the 43 training profiles. At each pressure level the water
vapor mixing ratio and temperature range are divided into a number of
bins and the number of training profiles falling within each bin is
shown for (a) temperature and (b) water vapor. Pressure
values up to 100 hPa are shown in (a).

Example of how the layer optical depth varies for (a)
fixed gases at a frequency of 730 cm-1 and layer pressures
between 102.5 and 85.18 hPa; (b) water vapor at a frequency of
1260.25 cm-1 and layer pressures between 521.46 and 478.54
hPa; (c) ozone at a frequency of 1034 cm-1 and layer
pressures between 253.71 and 222.94 hPa. The ordinates are defined
in Table 2.

Statistics of the difference between brightness
temperatures computed by use of the fast model and line-by-line
transmittances. The rms of the error for (a) water vapor plus
fixed gases, the dependent set of profiles for the water vapour and
fixed gases regression coefficients is used; (b) ozone, the
dependent set of profiles for the ozone regression coefficients is
used; (c) water vapor plus fixed gases and ozone for an independent
profile set.

Table 2

Definition of Profile Variables Used in Predictors Defined
in Table 3a

T(l) = [Tprofile(l + 1) + Tprofile(l)]/2

T*(l) = [Treference(l + 1) + Treference(l)]/2

W(l) = [Wprofile(l + 1) + Wprofile(l)]/2

W*(l) = [Wreference(l + 1) + Wreference(l)]/2

O(l) = [Oprofile(l + 1) + Oprofile(l)]/2

O*(l) = [Oreference(l + 1) + Oreference(l)]/2

P(l) = [pres(l + 1) + pres(l)]/2

Tr(l) = T(l)/T*(l)

δT(l) = T(l) - T*(l)

Wr(l) = W(l)/W*(l)

Or(l) = O(l)/O*(l)

Twl=∑i=2lPi-Pi-1]Tri-1

Wwl=∑i=1lPiPi-Pi-1Wi∑i=1lPiPi-Pi-1W*i

Owl=∑i=1lPiPi-Pi-1Oi∑i=1lPiPi-Pi-1O*j

Ouwl=∑i=1lOi∑i=1lO*j

OTwl=∑i=2lPiPi-Pi-1δTi-1Ori-1

a The pres(l)’s are the
values of the pressure at each
level. Tprofile(l),
Wprofile(l), and
Oprofile(l) are the temperature,
water vapor mixing ratio, and ozone mixing ratio
profiles. Treference(l),
Wreference(l), and
Oreference(l) are the
corresponding reference profiles. For these variables l
refers to the lth level; otherwise l is the
lth layer, i.e., the layer above the lth
level. Note that we take P(0) = 2P(1) -
P(2). Also Tw(1) = 0 and
OTw(1) = 0.

Table 3

Regression Predictors Used by the RTIASI for Fixed Gases,
Water Vapor, and Ozone

Predictor

Fixed Gases

Water Vapor

Ozone

Xj,1

sec(θ)

sec(θ)Wr
2
(j)

sec(θ)Or(j)

Xj,2

sec2(θ)

sec2(θ)Wr
2
(j)

sec(θ)Or(j)

Xj,3

sec(θ)Tr(j)

[sec(θ)Ww(j)]
2

sec(θ)Or(j)δT(j)

Xj,4

sec(θ)Tr
2
(j)

[sec(θ)Ww(j)]
4

[sec(θ)Or(j)]
2

Xj,5

Tr(j)

sec(θ)Wr(j)δT(j)

sec(θ)Or(j)δT(j)

Xj,6

Tr
2
(j)

sec(θ)Wr(j)

sec(θ)Or(j)
2
Ouw(j)

Xj,7

sec(θ)Tw(j)

4sec(θ)Wr(j)

OrjOuwjsecθOrj

Xj,8

secθTwjTrj

sec(θ)Wr(j)

secθOrjOwjOuwj

Xj,9

sec(θ)

[sec(θ)Wr(j)]
3

Or(j)sec(θ) Ouw(j)sec(θ)

Xj,10

sec(θ)4Tw(j)

Wr(j)

sec2(θ)Or(j) OTw(j)

Xj,11

0.0

sec(θ)Wr(j)δT(j)|δT(j)|

0.0

Xj,12

0.0

[sec(θ)Wr(j)]δT(j)

0.0

Xj,13

0.0

secθWrj2Ww

0.0

Xj,14

0.0

[secθWrj]WrjWwj

0.0

Tables (3)

Table 1

Minimum and Maximum Values of the Temperature, Water
Vapor, and Ozone Values Used in the Regression at Each Point of the
Pressure Layer Grid

Table 2

Definition of Profile Variables Used in Predictors Defined
in Table 3a

T(l) = [Tprofile(l + 1) + Tprofile(l)]/2

T*(l) = [Treference(l + 1) + Treference(l)]/2

W(l) = [Wprofile(l + 1) + Wprofile(l)]/2

W*(l) = [Wreference(l + 1) + Wreference(l)]/2

O(l) = [Oprofile(l + 1) + Oprofile(l)]/2

O*(l) = [Oreference(l + 1) + Oreference(l)]/2

P(l) = [pres(l + 1) + pres(l)]/2

Tr(l) = T(l)/T*(l)

δT(l) = T(l) - T*(l)

Wr(l) = W(l)/W*(l)

Or(l) = O(l)/O*(l)

Twl=∑i=2lPi-Pi-1]Tri-1

Wwl=∑i=1lPiPi-Pi-1Wi∑i=1lPiPi-Pi-1W*i

Owl=∑i=1lPiPi-Pi-1Oi∑i=1lPiPi-Pi-1O*j

Ouwl=∑i=1lOi∑i=1lO*j

OTwl=∑i=2lPiPi-Pi-1δTi-1Ori-1

a The pres(l)’s are the
values of the pressure at each
level. Tprofile(l),
Wprofile(l), and
Oprofile(l) are the temperature,
water vapor mixing ratio, and ozone mixing ratio
profiles. Treference(l),
Wreference(l), and
Oreference(l) are the
corresponding reference profiles. For these variables l
refers to the lth level; otherwise l is the
lth layer, i.e., the layer above the lth
level. Note that we take P(0) = 2P(1) -
P(2). Also Tw(1) = 0 and
OTw(1) = 0.

Table 3

Regression Predictors Used by the RTIASI for Fixed Gases,
Water Vapor, and Ozone